A vessel that travels across the surface of a liquid, for example a ship on an ocean or a boat on a lake, experiences resistance—drag—that opposes its movement across the liquid. This resistance has many different components that are each generated from a different source. For example, the viscosity of the liquid that contacts the vessel's hull as the hull moves relative to the liquid generates a viscous resistance component that is directly proportional to v2, which is the square of the vessel's speed. Another resistance component is generated by the vessel's hull pushing the liquid aside, and thus creating a wave, as the hull moves relative to the liquid. This wave resistance component represents energy that is absorbed by the liquid to generate the wave. Therefore, to move the vessel across the surface of the liquid, the vessel must be provided enough power to overcome the total resistance that the vessel experiences. If a resistance component is reduced, then the total resistance decreases, and thus less power will be required to move the vessel.
FIG. 1 is a typical graph of speed versus wave resistance and viscous resistance for two similar hulls whose only significant difference is their length. The contour 15 illustrates the general relationship between wave resistance and speed for the shorter hull. The contour 16 illustrates the general relationship between wave resistance and speed for the longer hull. The contour 17a illustrates the relationship between viscous resistance and speed for the shorter hull. The contour 17b illustrates the relationship between viscous resistance and speed for the longer hull.
As shown in FIG. 1, the maximum wave resistances 18a and 18b are close in magnitude, and the viscous resistances 17a and 17b increase as the speed of the hull increases and are also close in magnitude. In addition, and as discussed in greater detail in conjunction with FIGS. 2C and 2D, the maximum wave resistance 18a for the shorter hull occurs at a speed that is less than the speed at which the maximum wave resistance 18b occurs for the longer hull.
FIG. 2A is a typical graph of total resistance versus speed for the two hulls referenced in FIG. 1. The contour 19a illustrates the general relationship for the shorter hull, and is generated by adding the resistance value in each of the contours 15 and 17 of FIG. 1 that correspond to the same speed. The region 19b of the contour 19a corresponds to the total resistance when the maximum wave resistance 18a (FIG. 1) occurs. The contour 19c illustrates the general relationship for the longer hull, and is generated by adding the resistance value in each of the contours 16 and 17 of FIG. 1 that correspond to the same speed. The region 19d of the contour 19c corresponds to the total resistance when the maximum wave resistance 18b (FIG. 1) occurs.
FIG. 2B is a typical graph of power versus speed for the two hulls referenced in FIGS. 1 and 2A. The contour 21a illustrates the general relationship between speed and the amount of power required to maintain the speed for the shorter hull. The region 21b of the contour 21a corresponds to the amount of power at the speed that the shorter hull generates a maximum wave resistance 18a (FIG. 1). The contour 21c illustrates the general relationship between speed and the amount power required to maintain the speed for the longer hull. The region 21d of the contour 21c corresponds to the amount of power at the speed that the longer hull generates a maximum wave resistance 18b (FIG. 1). Power is related to total resistance and speed, and can be expressed by the mathematical relationship:
  P  =            (              R        ×        v            )        550  
where P=power in horsepower, R=resistance in pounds, and v=speed in feet/second.
As shown in FIG. 2B at slow speeds, speeds slower than the speed 23, the shorter hull requires more power to maintain its speed than the longer hull requires to maintain the same speed. But at fast speeds, speeds faster than the speed 23, the shorter hull requires less power to maintain its speed than the longer hull requires to maintain the same speed. Furthermore, the shorter hull requires less power to accelerate through its maximum-wave-resistance speed 25a than the longer hull requires to accelerate through its maximum-wave-resistance speed 25b because the total resistance and the speed 25a are significantly less than the total resistance and the speed 25b. 
For any hull shape, the speed at which the hull experiences a maximum wave resistance can be estimated by calculating the Froude number. The Froude number F is a measure of the hull's velocity through the liquid relative to the hull's length, and is mathematically defined as follows:
  F  =      v                  g        ⁢                                  ⁢        l            
where F=Froude number, v=hull speed relative to the liquid, g=acceleration of gravity, and l=hull length. The Froude number is unitless, and thus the units of v, g, and l are selected such that the square root of g multiplied by l produces the same unit as v. As shown in the equation, the Froude number is inversely proportional to the square root of the hull's length, and directly proportional to the hull's speed relative to the liquid.
FIG. 2C is a typical graph of wave resistance (Rw) versus Froude number for a hull moving in water, and illustrates the general relationship between wave resistance and Froude number. The length of the hull and the acceleration of gravity is the same for each Froude number in the graph. Thus, each Froude number corresponds to the hull's velocity relative to the liquid. Every moving hull has a unique graph that represents the relationship between the wave resistance that the hull experiences and the Froude number that the hull generates. Although the specific contour of the relationship (the graph) may vary from one hull to another, the general contour of the relationship is similar for most hulls. For example, every contour includes three regions, a low Froude number region 20 where the Froude number is less than 0.4, a hump region 22 where the Froude number is within the range 0.4 to 0.6, and a high Froude number region 24 where the Froude number is greater than 0.6.
As shown in FIG. 2C, when a hull's velocity generates a Froude number in the low Froude number region 20, the wave resistance is relatively low. Increasing the velocity of the hull to other Froude numbers in this Froude number region will proportionally and moderately increase the wave resistance that the hull experiences. When the hull's velocity generates a Froude number of approximately 0.4, increasing the hull's velocity, exponentially increases the wave resistance that the hull experiences. When the hull's velocity generates a Froude number near 0.5, the hull experiences the maximum wave resistance 26. This maximum 26 occurs when the wavelength of the wave generated by the hull is approximately equal to two times the length of the hull, and is often referred to as the resistance or powering “hump”. But when the hull's velocity generates a Froude number greater than approximately 0.5, the wave resistance begins to decrease, and the hull experiences less wave resistance causing a further increase in the hull's velocity until the other components of drag, such as viscous drag, sufficiently increase to stop the hull's acceleration.
FIG. 2D is a typical graph of wave resistance (Rw) versus speed for two similar hulls whose only significant difference is their length. The graph illustrates the general relationship between the maximum wave resistance and the speed that the maximum wave resistance occurs. The relationship between wave resistance and speed for the shorter hull is shown by the contour 28. The relationship for the longer hull is shown by the contour 30. The maximum wave resistance for each 32 and 34 occurs at a speed that generates a Froude number of approximately 0.5.
As shown in FIG. 2D, the shorter hull's maximum wave resistance 32 occurs at a speed slower than the speed at which the longer hull's maximum wave resistance 34 occurs. Due to the shorter hull's larger cross-sectional area, which is required to provide a displacement that is equal to the longer hull's displacement, the shorter hull's maximum wave resistance 32 may also be greater than the longer hull's maximum wave resistance 34. Because the maximum wave resistance for most hulls occurs when the speed of the hull generates a Froude number approximately 0.5, the speed at which the hull experiences the maximum wave resistance depends on the length of the hull. Therefore, as the length of the hull increases, the speed at which the hull experiences the maximum wave resistance also increases. And as the length of the hull decreases, the speed at which the hull experiences the maximum wave resistance also decreases.
Referring back to FIG. 2C, the hump region 22 is where the greatest amount of power provided to the hull is lost to generating waves, and is thus unavailable to increase the speed of the hull. Because of this, conventional large vessels, such as commercial freighters, are designed to avoid the hump region 22 and cruise at a speed that generates a Froude number less than about 0.4. To increase the cruising speed of these vessels while remaining in the low Froude number region, the hulls of these vessels are lengthened.
For example, FIG. 3 is a side view of a conventional ship 36 having a hull length 38. The ship 36 is designed to cruise at a speed that generates a Froude number equal to about 0.4. If a greater cruising speed is desired, one can design the ship's hull to be longer such that the Froude number at the cruising speed remains equal to about 0.4. For example, if the length 38 is 200 feet, then the cruising speed that generates a Froude number equal to 0.4 is about 18.9 knots. If the length 38 is 400 feet, then the cruising speed that generates a Froude number equal to 0.4 is about 26.8 knots.
Unfortunately, because conventional large vessels are designed to cruise at speeds that generate a Froude number less than about 0.4, the effective speed limit for these vessels is the speed that generates a Froude number approximately 0.4. To exceed this speed limit, the vessel requires a substantial increase in power to overcome the wave resistance that occurs while moving at a speed that generates a Froude number greater than about 0.4 but less than about 0.5. Moreover, because the hulls of such vessels are lengthened to increase their cruising speed in the low Froude number region, the maximum wave-resistance that they experience at a Froude number approximately 0.5 will occur at a relatively high speed. Thus, the vessel would require a large amount of power (21b in FIG. 2B) to overcome the total resistance (19b in FIG. 2A) at the maximum-wave-resistance speed, and to power the vessel at a cruising speed that is in the high Froude number region (24 in FIG. 2C). Consequently, the size and weight of the vessel's propulsion system would significantly increase, and thus reduce the total payload of the vessel and increase fuel consumption.
Referring again to FIG. 2C, many boats have hulls that plane on the surface of the water while the boat cruises. These boats typically have a hull that extends continuously for the length of the boat and are provided with enough power to propel the boat through the hump region 22. In the high Froude number region 24, the boat's hull planes or develops lift from dynamic forces of the water. This planing effect lifts the boat, reducing the wetted surface area of the hull in contact with the water, and thus reducing viscous resistance. Additionally, this planing effect reduces the boat's displacement, which reduces wave resistance. Unfortunately, because the hull length of large, conventional planing vessels is long, the hump region 22 occurs at a high speed. This high speed generates a significant viscous resistance component of the total resistance, which causes the total resistance through the hump region 22 to be high. Thus, a large amount of power is required to propel the boat through the hump region to reach its cruising speed.